A study of working actors looked at age and gender. One sample of 65 male actors had a mean age of 23 and a standard deviation of 2. The other sample included 65 female actors with a mean age of 30 and a standard deviation of 5. Estimate with $97 \%$ confidence the difference between the average ages of working male $\left(\mu_{1} ight) $ and female $\left(\mu_{2} ight) $ actors. Round answers to the nearest hundredth. $$